DSL is a technology for bringing high-bandwidth information to homes and small businesses over ordinary copper telephone lines. xDSL refers to different variations of DSL, such as ADSL, HDSL, and RADSL. If a home or small business is close enough to a telephone company central office that offers DSL service, data might be received at rates up to 6.1 megabits (millions of bits) per second (of a theoretical 8.448 megabits per second), enabling continuous transmission of motion video, audio and even 3-D effects. More typically, individual connections will provide from 1.544 Mbps to 512 Kbps downstream and approximately 128 Kbps upstream. A DSL line can carry both data and voice signals, with the data part of the line being continuously connected.
Traditional phone service (sometimes called POTS for “plain old telephone service”) connects a home or small business to a telephone company office over copper wires that are wound around each other, and typically called a twisted pair. An input device (such as a phone set) takes an acoustic signal (which is a natural analog signal) and converts it into an electrical equivalent in terms of volume (signal amplitude) and pitch (frequency of wave change). The signaling of the telephone company is already configured for analog wave transmissions, so this approach has been very effective in transferring information back and forth between a signaling device and the telephone company. A computer, however, must have a modem to demodulate the analog signal and convert signaling values into the typical string of “0” and “1” values which serve as digital information.
Such analog transmissions use only a small portion of the available amount of information that could be transmitted over copper wires, and hence the maximum amount of data that can be received using ordinary modems is about 56 Kbps (thousands of bits per second). Later technologies, including Integrated Services Digital Network (ISDN), can receive data at speeds up to 128 Kbps. In general, the ability of a computer to receive information is constrained by several factors, including the following: the telephone company applies filtering to information that arrives as digital data; the information is transformed into analog form for transmission over the telephone line; and the transmission requires a modem to change the analog signal information back into digital information.
DSL uses a much wider bandwidth for transmitting data. Additionally, the digital signal can be separated from the voice signal and shifted upwards on the transmission band. The overall bandwidth can be simultaneously used to transmit an analog (voice) signal and digital data signal over the same data line. Asymmetric Digital Subscriber Line (ADSL) is asymmetric in that it uses most of the channel to transmit downstream to the user, and only a small part to receive information from the user. ADSL is generally offered at downstream data rates from 512 Kbps to about 6 Mbps. ADSL was specifically designed to exploit the one-way nature of most multimedia communication in which large amounts of information flow toward the user, and only a small amount of interactive control information is returned.
To connect to a DSL source (i.e., DSL, ADSL, or otherwise), a DSL modem is needed. Various modulation schemes can be used in such modems. Discrete multitone (DMT) modulation is a common method of separating a DSL signal so that the usable frequency range is separated into 256 frequency bands (or channels) of 4.3125 KHz each. DMT generally uses the fast Fourier transform (FFT) algorithm for modulation and demodulation. Examples of devices which employ the DMT method of modulation include ADSL modems that conform to ITU-T Recommendations G.992.1 and G.992.2. The ITU-T (which is the Telecommunication Standardization Sector of the International Telecommunications Union) is the primary international body for fostering cooperative standards for telecommunications equipment and systems. Other modulation technologies for DSL include carrierless amplitude modulation (CAP) and multiple virtual line (MVL).
DMT modems transmit information coded in symbols consisting of blocks of length N of time-domain samples (typical values of N are 256 and 512). The fundamental algorithms used to process these symbols are based on the Discrete Fourier Transform (DFT). A fundamental assumption underlying use of the DFT is that the signals being processed are periodic and of finite duration. DMT symbols satisfy neither of these conditions. Further, transmitting DMT symbols through an analog channel convolves the symbols with the unit-sample response of the channel. Referring now to FIG. 1A, a representative unit response h(n) (100) is shown, with N being the time index. This unit-sample response has a duration that is an appreciable fraction of N (102). As result, the samples that are transmitted as part of one symbol appear combined with samples of the succeeding symbol. This phenomenon is called Intersymbol Interference (ISI).
DMT modems typically use two techniques to mitigate the effect of ISI: a cyclic prefix, and a time-domain equalizer (TEQ). The cyclic prefix concept, as written into the DMT modem standards, calls for increasing the length of each symbol by a small number of samples (i.e., C, shown as 104). These extra samples can then be ignored by the receiving modem, given that they are expected to be polluted with ISI. These additional samples, however, are wasted from the point of view of transmitting information. As a result, C should be kept small relative to N. In practice, the value of C is about 6% to 8% of N. This is much less than the true length of the unit-sample response of physical channels. Therefore, the cyclic prefix modem often includes an additional component, the TEQ, to shorten the length of the composite channel/TEQ unit-sample response to an acceptable value.
Adaptive equalizers for telephone channels are known, but the problem of shortening the length of the composite response (i.e., channel response plus TEQ unit-sample response) is different than problems faced by modems that employ adaptive equalizers. In simpler terms, adaptive equalizers normally are designed such that the convolution of the channel unit-sample response with that of the adaptive equalizer yields a single unit-impulse, thereby eliminating ISI. Because DMT modems perform further equalization in the frequency domain during later steps of signal processing the receiver, the requirements on the TEQ are different from those placed, for example, on the adaptive equalizers used in voice-band modems. The normal adaptive equalizer works to shorten the length of the composite unit-sample response to one; the TEQ works to shorten the composite unit-sample response to a value less than, or equal to, C. FIG. 1B shows a graphical example of the composite unit response h(n)*a(n) (106) being shortened to a value approximately less than C (104).
In practice, the analog channel is generally unknown before the modem is installed on a given DSL. Therefore the TEQ must be designed on the fly using algorithms that learn the characteristics of the analog channel and synthesize the appropriate TEQ. Known prior art includes the following: Chow, J. S.; Cioffi, J. M.; Bingham, J. A. C.—“Equalizer training algorithms for multicarrier modulation systems,” Conference Record of IEEE International Conference on Communications, Geneva, Vol. 2, 1993. This reference describes an iterative method that uses frequency-domain calculations to derive the TEQ. The frequency-domain method is problematic as it does not guarantee convergence to a solution. Moreover, the iterative nature of the process requires certain judgments to be performed along the way in order to reach a workable solution.
Accordingly, what is needed in the field of art is a non-iterative method of designing a TEQ for a DSL modem, and in particular, a method applicable to an ADSL (or other type) modem that employs DMT. This non-iterative method should provide a solution wherein the output of the TEQ has a duration less than C and a solution that is deterministic without concerns of non-convergence.